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Questions tagged [probability]

For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].

The probability that an event occurs is a number in the interval $[0, 1]$, which represents how likely the event is to happen. $0$ indicates it will never happen, $1$ indicates it will always happen.

For example, throwing two dice gives a total of $6$ five times out of thirty-six. We write $$P(X=6)=\frac{5}{36}$$.

Use this tag for basic questions about probability, independence, total probability and conditional probability.

For questions about the theory of probability, use instead. For questions about specific probability distributions, use .

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Independent or dependent events, drawing cards without replacement

Firstly, i want to sorry for asking the question that has been answered. This is because i don't have enough reputation so that i can ask the people who gave the answer. The question that has been answered: Independent events, drawing cards without…
Alex
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Variance of the number of balls between two specified balls

Question: Assume we have 100 different balls numbered from 1 to 100, distributed in 100 different bins, each bin has 1 ball in it. What is the variance of the number of balls in between ball #1 and ball #2? What I did: I defined $X_i$ as an…
jreing
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Covariance and variance of a Poisson r.v.

Given a Poisson process $N(t),t\geq 0$ with rate $\lambda$ and another r.v. $T$ independent of $N(t)$ with mean $\mu$ and variance $\sigma^2$, I would like to compute the following quantities: $$ \mathbb{Cov}(T,N(T)) \ \ \mbox{ and } \ \…
Dan
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Expected number of different colors

I have a box containing $n$ colored balls. There are $c$ different colors. $k_1$ balls have color $1$, $k_2$ balls have color $2$, ... and $k_c$ balls have color $c$. When I draw $m$ balls with replacement, what is the expected number of different…
wnvl
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Central Limit Theorem

If N is a poisson random variable, why is the following true? It is from "Probability and Stochastic Processes" by Yates, page 301, equation 8.2 to 8.3 $$ P\left(\left|\frac{N-E(N)}{\sigma_N}\right| \geq \frac{c}{\sigma_N}\right) = P(|Z| \geq…
jrand
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Compute the probability that the outcome of a die's fifth throw is one of the previous 4

A die is randomly rolled five times, the probability that outcome of the fifth throw is one of the outcomes of the first 4 throws is? Attempt: For first 4, there are following possibilities: (after that we will multilply the possibilities for the…
Archer
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How many monkeys do I need to have a 95% chance of producing Shakespeare's Romeo and Juliet within one year?

I've heard of the analogy that infinite monkeys with typewriters will eventually produce Shakespeare's Romeo and Juliet, but what if, instead of "eventually", I want "one year". How many monkeys do I need to produce Romeo and Juliet within one…
user649958
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Under what conditions does $E[f(X)] \approx f(E[X])$?

Intuitively, when a random variable $X$ has a low variance, a sufficiently smooth function of that random variable will have an expected value which is close to that same function applied to $E[X]$. That is, $$ f(E[X]) \approx E[f(X)] $$ This is…
Display Name
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Sum of three independent random variables

Let $X$, $Y$, and $Z$ be independently and identically distributed variables, each uniformly distributed between $0$ and $2$. What is the probability that $X+Y+Z\leq2$? All the other answers on similar questions refer to various things like…
Prasiortle
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What is the probability that the bacteria population eventually dies out?

A jar begins with one bacteria. Every minute, every bacteria turns into 0, 1, 2, or 3 bacteria with a probability of 25% for each case (dies, does nothing, splits into 2, or splits into 3). What is the probability that the bacteria population…
mathaholic
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From an urn containing a white and b black balls, balls are successively drawn without replacement until only those of the same colour are left.

From an urn containing a white and b black balls, balls are successively drawn without replacement until only those of the same colour are left. What is the probability that balls left are white? This is what I have…
Abhishek Ghosh
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Probability of covering all vertices of a square

Let $~A_1 = (0,0), ~~A_2 = (1,0),~~ A_3 = (1,1)~$ and $~A_4 = (0,1)~$ be the four vertices of a square. A particle starts from the point $~A_1~$ at time $~0~$ and moves either to $~A_2~$ or to $~A_4~$ with equal probability. Similarly, in each of…
debdutt
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Two type of balls in a bag

In a bag there are $15$ red and $5$ white balls. Two balls are chosen at random and one is found to be red. The probability that the second one is also red is? I have attempted this question by counting all the favorable cases: Both red…
user619072
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A coin is weighted, such that the probability of heads in any given toss is twice that of tails.

A coin is weighted, such that the probability of heads in any given toss is twice that of tails. A player tosses two such coins. The player wins £4 if 2 tails occur and £1 if 1 tail occurs. The player should lose less than what amount of money if no…
user611414
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Your evil probability professor has an urn with 9 balls.

Your evil probability professor has an urn with 9 balls: 2 red, 3 white and 4 blue. He draws two balls from the urn without replacement. Let X be the number of red balls drawn and Y the number of white balls. a) Determine the joint probability…
TFAE
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